Mister Exam

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Sum of series:
1/2^(2n-2)
(6+(-4)^n)/(7^(n+2))
x²-16
ln(1-(1/(k)^2))
Identical expressions
2i+ one /n
2i plus 1 divide by n
2i plus one divide by n
2i+1 divide by n
Similar expressions
(2*i+1)/n^2
(2i+1)/n^2
2i-1/n

Sum of series/ 2i+1/n

Sum of series 2i+1/n

The solution

You have entered [src]

  oo           
 ___           
 \  `          
  \   /      1\
   )  |2*i + -|
  /   \      n/
 /__,          
i = 1

$$\sum_{i=1}^{\infty} \left(2 i + \frac{1}{n}\right)$$

Sum(2*i + 1/n, (i, 1, oo))

The radius of convergence of the power series

Given number:
$$2 i + \frac{1}{n}$$
It is a series of species
$$a_{i} \left(c x - x_{0}\right)^{d i}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{i \to \infty} \left|{\frac{a_{i}}{a_{i + 1}}}\right|}{c}$$
In this case
$$a_{i} = 2 i + \frac{1}{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{i \to \infty} \left|{\frac{2 i + \frac{1}{n}}{2 i + 2 + \frac{1}{n}}}\right|$$
Let's take the limit
we find

True

False

The answer [src]

     oo
oo + --
     n

$$\infty + \frac{\infty}{n}$$

oo + oo/n

Examples of finding the sum of a series

The Sum of the Power Series
```
x^n/n
```
```
(x-1)^n
```
Factorial
```
1/2^(n!)
```
```
n^2/n!
```
```
x^n/n!
```
```
k!/(n!*(n+k)!)
```
Flint Hills Series
```
csc(n)^2/n^3
```
Basel problem
```
1/n^2
```
```
1/n^4
```
```
1/n^6
```
Harmonic series
```
1/n
```
Grandi's series
```
(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
```
(3*n - 1)/(-5)^n
```
```
(-1)^(n - 1)*n/(6*n - 5)
```
Newton–Mercator series
```
(-1)^(n + 1)/n*x^n
```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```

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Identical expressions

Similar expressions

Sum of series 2i+1/n

The solution

Examples of finding the sum of a series